Theorem REF  almost readily yields our main result.
For a formal argument, we use the framework based on interpretation schemes from [1]},
which we now briefly overview.
Let \(\kappa \)  and \(\lambda \)  be two signatures
where \(\lambda \)  has \(\ell \)  relational symbols \(R_1,\ldots ,R_\ell \)  with arities \(r_1,\ldots ,r_\ell \) .
A (first order) interpretation scheme \(I\)  of \(\lambda \) -structures in \(\kappa \) -structures
consists of a first order \(\kappa \) -formula \(\Phi _0\)  with one free variable and
first order \(\kappa \) -formulas \(\Phi _i\) , each with \(r_i\)  free variables.
If \(K\)  is a \(\kappa \) -structure, then \(I(K)\)  is the \(\lambda \) -structure with the domain \(\lbrace x\in K:\Phi _0(x)\rbrace \)  and
\(R_i=\lbrace (x_1,\ldots ,x_{r_i})\in K^{r_i}:\Phi _i(x_1,\ldots ,x_{r_i})\rbrace \) .
We say that the relational symbol \(R_i\)  is interpreted trivially by a relational symbol \(Q\)  (from the signature \(\kappa \) )
if \(\Phi _i(x_1,\ldots ,x_{r_i})=Q(x_1,\ldots ,x_{r_i})\) .
The following lemma from [1]} links modelings of \(\kappa \) -structures and \(\lambda \) -structures.
